Response of superconducting weak links to photons

Volume 33A, number 3

RESPONSE

PHYSICS L E T T E R S

OF

SUPERCONDUCTING

WEAK

19 October 1970

LINKS

TO

PHOTONS

R. Y. CHIAO*

Department of Physics, University of California, Berkeley, California, U.S.A. Received 16 September 1970

A theoretical study of radiation detectors using superconducting weak links has been undertaken, with the Mercereau ring interferometer as a specific example. A sing[e photon should depress the critical current fractionally by 27t~ ~ 4.6%. These detectors should possess sizeab[e post-detection gains, so that individual photons should be countable.

T h e r e a r e two different types of r a d i a t i o n det e c t o r s involving s u p e r c o n d u c t i n g weak links: the f i r s t places a weak link at a high impedance or voltage m a x i m u m point in a m i c r o w a v e cavity, the second places a weak link at a low impedance or c u r r e n t m a x i m u m point in a cavity [1]. We shall r e p o r t h e r e on the t h e o r e t i c a l r e s u l t s conc e r n i n g the f i r s t type of detector. An example of the f i r s t type involves a M e r c e r e a u r i n g i n t e r f e r o m e t e r s u r r o u n d i n g a magnetic field m a x i m u m in a cavity or r e s o n a t o r (e.g. a d i e l e c t r i c c y l i n d e r with a M e r c e r e a u ring a r o u n d it). This r i n g d e t e c t s the magnetic flux g e n e r a t e d by i n c o m i n g radiation. A single photon in the cavity c a u s e s a f r a c t i o n a l d e p r e s s i o n in the c r i t i c a l c u r r e n t of the i n t e r f e r o m e t e r of roughly 2 ~ ~ ~ 4.6% where ~ is the fine s t r u c t u r e constant. The detection p r o c e s s involves the m e a s u r e m e n t of the c r i t i c a l c u r r e n t whose value depends on the state of the r a d i a t i o n field. Hence the c r i t i c a l c u r r e n t b e c o m e s a quantum m e c h a n i c a l operator:

2t o exp(-lraK 2 Z

Zo ) ~ l n )

Ln

K2Z ~o)(

i s filled with blackbody r a d i a t i o n at t e m p e r a t u r e T r a d , one gets an expectation value for the c r i tical current: (Ic)b. b. = 2io e x p ( _ 2 ~ a

K2 Z [ ,

Z--°

1

-2+exp (~w/kTrad)-i

]

)

In another s p e c i a l case when the cavity is filled with coherent r a d i a t i o n of n a v e r a g e photon n u m b e r one gets: co h =

Z 2I o e x p ( - T r ~ K 2 Z o )

IJo ((81r~

K2 Z ~)1/2)t Zo

where Jo is the z e r o - o r d e r B e s s e t function, a g r e e i n g with J o s e p h s o n ' s c l a s s i c a l r e s u l t [2] in the l i m i t ~ ~ oo.

n[

where 2 I is the c r i t i c a l c u r r e n t in the a b s e n c e o of r a d i a t i o n , ~ is the f i n e - s t r u c t u r e constant, K i s the flux-coupling efficiency between the c a vity and the i n t e r f e r o m e t e r , Z is the impedance of the cavity (i.e.(L/C) 1/2 for a tank circuit), Z o is the i m p e d a n c e of f r e e space, < n ] is the n-photon state, and L n i s the n t h o r d e r L a g u e r r e polynomial. In the special case when the cavity * Work partially supported by the National Aeronautics and Space Administration Grant NGL-05-003-272. :~ A[fred P. Sloan Fel[ow.

C

Fig. 1. An equivalent circuit diagram for the coupling of a Mercereau interferometer to a microwave cavity described in the text. The resistance R may be Ohmic or radiative {e.g. due to a coupling hole). 177

Volume 33A. n u m b e r 3

/°ItYSICS

04

o

LFTTEttS

19 October t970

a m p l i f i e r of t h e d e t e c t e d s i g n a l . T h e e n e r g y of a s i n g l e p h o t o n w i l l b e a m p l i f i e d by a p o s t - d e t e c t i o n g a i n of

03

1

C

.4

/ . :; ~ , 2 Z °

Q;

.d 02

t~

u~

~

--

u

.

~.

Coherent

.

rad,ahon

01

0

I

2

3

Average

photon

number

4 in

S

cavity

Fig. 2. A plot of the c r i t i c a l c u r r e n t ( l e) v e r s u s a v e r age photon n u m b e r ,1 in the cavity (i.e. intensity of r a diation) for the two special c a s e s of blackbody r a d i a tion and c o h e r e n t radiation d e s c r i b e d in tile text. For blackbody radiation ( 1c) = 210 exp (-'t') exp (- 23k) where ~ t / ( e x p (hoo/l'Tr_qd) - t) and 3 rr c~ K 2 Z/Z,, for coherent r a d i a t i o n ( / C~} 210 e x p ( - 7 ) . 1 O {(~q'),~)[721,' ' For t h e s e plots, we have taken ~' 1.

This type of detector

is a l s o a very low noise

THEORETICAL CARBON

TRANSITION 3p-3D

b e f o r e b e i n g d e l i v e r e d to t h e f i r s t r o o m - t e m p e r a t u r e a m p l i f i e r . H e r e z, i s t h e g a p e n e r g y . T h u s t h e s i g n a l - t o - n o i s e f o r t h e d e t e c t i o n of i n d i v i d u a l photon pulses is SIN-- Gh~,/kTam p where Tam p i s t h e n o i s e t e m p e r a t u r e of t h e f i r s t r o o m temperature amplifier. The fact that Johnson noise fluctuations at liquid helimn temperatures have been observed with good signal-to-noise u s i n g t h e r i n g i n t e r f e r o m e t e r [3] i n d i c a t e s t h a t this gain is sufficiently large, g the fluctuations d u e to h T b a t h a r e d e t e c t a b l e , t h e n f l u c t u a t i o n s d u e to h v > h T b a t h s h o u l d b e d e t e c t a b l e , i.e. i n dividual photons should be countable.

Re~c~'cnccs [ l l f I . Y . Chiao. Bull, Am. [21 B. D. Joseph,son. Phys. Advan. Phys. 14 (1965) [31 J. E. M e r e e r e a u . to be

PROBABILITIES

ISOELECTRONIC

t'hys. Soc. t5 (t970) 3!). L e t t e r s t (1962) 251: 419. published.

FOR

THE

SEQUENCE

C . N I C O L A I D E S a n d O. S I N A N O G L U * SIc~'IDG, C/~c,H.,elry l,ahr)raloKv. Yah' {,',iucr,~'ilv NeTr fla~'~'~, (?o~z~z, I~;:=i"~. ( SA

Heceived t August 1970

T h e o r e t i c a l multiplet oscillatoc streng-ths are calculated for the CI. Nil, OlI1 3 p - 3 l ) lines using a new theory of atomic s t r u c t u r e including e l e c t r o n c o r r e l a t i o n . The r e s u l t s a g r e e v e t 3 well with recent experiments.

There is a number of experimental results on the transition probability of the ls 2 2s 2 2p 2 3p ls 2 2s2p 3 3D line in the CI. NIl, and OIII ions. Intensity measurements from emission arc experiments [I] as well as lifetime measurements by the phase shift [2] and beam-foil techniques [3-51 have provided quite accurate values. The line has also attracted the attention of the theor178

ists. A very limited configuration-interaction (only two c o n f i g u r a t i o n s c o n s i d e r e d ) w a s f i r s t p e r f o r m e d b y B o l o t i n e t a l . [6]. C o h e n a n d D a l garno approached the problem by a Z-expansion p e r t u r b a t i o n t h e o r y [7}. T h e n e u t r a l c a r b o n l i n e * Work supported by a g r a n t from tile US National Science Foundation.